Polarisation effects in multiple scattering photon calculations using the Boltzmann vector equation

Studies on radiative transfer lead to a clean formulation of polarised photon transport in terms of the vector Boltzmann equation whose solution gives the four Stokes components of the flux, from which the full polarisation state of the photons can be determined at any given position, wavelength (energy) and solid angle. One of the relevant results observed during the formulation of the vector transport equation is the partial coverage of the wave properties of the photons with this model. In fact, even if the Boltzmann vector equation is an important step forward for the description of radiative transfer with respect to the scalar approach used to describe 'particle'-like photons, it is still insufficient to provide a whole description of an important phase-related property like coherence. In this sense, the above vector equation seems to be appropriate for describing photon beams which add incoherently among them, but not for describing coherent interference. Up to now, coherence has been described independently to the transport equation, as an additive term to the vector solution valid for diffuse incoherent radiation. New approaches are being investigated in order to include the concept of coherence into the vector transport equation. In this article, a summary view of the evolution of the Boltzmann transport equation will be provided, first from scalar to vector, to take care of the description of the evolution of the polarization state. Secondly the present state of the treatment of coherence will be considered. Finally, the state-of-the-art description of multiple scattering involving Rayleigh scattering will be discussed, in the framework of both reflection and transmission experiments.